%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:22:03 PM UTC 2026
% Result : Theorem 0.09s 0.51s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU225+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 06:00:05 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.51 % Refutation found
% 0.09/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.51 % SZS output start CNFRefutation for theBenchmark
% 0.09/0.51 fof(f7,axiom,(
% 0.09/0.51 (! [A] :( ( relation(A)& function(A) )=> (! [B,C] :( ( in(B,relation_dom(A))=> ( C = apply(A,B)<=> in(ordered_pair(B,C),A) ) )& ( ~ in(B,relation_dom(A))=> ( C = apply(A,B)<=> C = empty_set ) ) ) )) )),
% 0.09/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f9,axiom,(
% 0.09/0.51 (! [A,B] :( relation(A)=> relation(relation_dom_restriction(A,B)) ) )),
% 0.09/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f19,axiom,(
% 0.09/0.51 (! [A,B] :( ( relation(A)& function(A) )=> ( relation(relation_dom_restriction(A,B))& function(relation_dom_restriction(A,B)) ) ) )),
% 0.09/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f24,axiom,(
% 0.09/0.51 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,relation_dom(relation_dom_restriction(C,A)))<=> ( in(B,relation_dom(C))& in(B,A) ) ) ) )),
% 0.09/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f42,axiom,(
% 0.09/0.51 (! [A,B] :( ( relation(B)& function(B) )=> (! [C] :( ( relation(C)& function(C) )=> ( B = relation_dom_restriction(C,A)<=> ( relation_dom(B) = set_intersection2(relation_dom(C),A)& (! [D] :( in(D,relation_dom(B))=> apply(B,D) = apply(C,D) ) )) ) ) )) )),
% 0.09/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f44,conjecture,(
% 0.09/0.51 (! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,A)=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ) )),
% 0.09/0.51 file('/export/starexec/sandbox/benchmark/theBenchmark.p')).
% 0.09/0.51 fof(f45,negated_conjecture,(
% 0.09/0.51 ~((! [A,B,C] :( ( relation(C)& function(C) )=> ( in(B,A)=> apply(relation_dom_restriction(C,A),B) = apply(C,B) ) ) ))),
% 0.09/0.51 inference(negated_conjecture,[status(cth)],[f44])).
% 0.09/0.51 fof(f60,plain,(
% 0.09/0.51 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|(C=apply(A,B)<=>in(ordered_pair(B,C),A)))&(in(B,relation_dom(A))|(C=apply(A,B)<=>C=empty_set)))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f7])).
% 0.09/0.51 fof(f61,plain,(
% 0.09/0.51 ![A]: ((~relation(A)|~function(A))|(![B,C]: ((~in(B,relation_dom(A))|((~C=apply(A,B)|in(ordered_pair(B,C),A))&(C=apply(A,B)|~in(ordered_pair(B,C),A))))&(in(B,relation_dom(A))|((~C=apply(A,B)|C=empty_set)&(C=apply(A,B)|~C=empty_set))))))),
% 0.09/0.51 inference(NNF_transformation,[status(thm)],[f60])).
% 0.09/0.51 fof(f62,plain,(
% 0.09/0.51 ![A]: ((~relation(A)|~function(A))|((![B]: (~in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|in(ordered_pair(B,C),A)))&(![C]: (C=apply(A,B)|~in(ordered_pair(B,C),A))))))&(![B]: (in(B,relation_dom(A))|((![C]: (~C=apply(A,B)|C=empty_set))&(![C]: (C=apply(A,B)|~C=empty_set)))))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f61])).
% 0.09/0.51 fof(f65,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|~X2=apply(X0,X1)|X2=empty_set)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f62])).
% 0.09/0.51 fof(f68,plain,(
% 0.09/0.51 ![A,B]: (~relation(A)|relation(relation_dom_restriction(A,B)))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f9])).
% 0.09/0.51 fof(f69,plain,(
% 0.09/0.51 ![A]: (~relation(A)|(![B]: relation(relation_dom_restriction(A,B))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f68])).
% 0.09/0.51 fof(f70,plain,(
% 0.09/0.51 ![X0,X1]: (~relation(X0)|relation(relation_dom_restriction(X0,X1)))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f69])).
% 0.09/0.51 fof(f87,plain,(
% 0.09/0.51 ![A,B]: ((~relation(A)|~function(A))|(relation(relation_dom_restriction(A,B))&function(relation_dom_restriction(A,B))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f19])).
% 0.09/0.51 fof(f88,plain,(
% 0.09/0.51 ![A]: ((~relation(A)|~function(A))|((![B]: relation(relation_dom_restriction(A,B)))&(![B]: function(relation_dom_restriction(A,B)))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f87])).
% 0.09/0.51 fof(f90,plain,(
% 0.09/0.51 ![X0,X1]: (~relation(X0)|~function(X0)|function(relation_dom_restriction(X0,X1)))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f88])).
% 0.09/0.51 fof(f100,plain,(
% 0.09/0.51 ![A,B,C]: ((~relation(C)|~function(C))|(in(B,relation_dom(relation_dom_restriction(C,A)))<=>(in(B,relation_dom(C))&in(B,A))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f24])).
% 0.09/0.51 fof(f101,plain,(
% 0.09/0.51 ![A,B,C]: ((~relation(C)|~function(C))|((~in(B,relation_dom(relation_dom_restriction(C,A)))|(in(B,relation_dom(C))&in(B,A)))&(in(B,relation_dom(relation_dom_restriction(C,A)))|(~in(B,relation_dom(C))|~in(B,A)))))),
% 0.09/0.51 inference(NNF_transformation,[status(thm)],[f100])).
% 0.09/0.51 fof(f102,plain,(
% 0.09/0.51 ![C]: ((~relation(C)|~function(C))|((![A,B]: (~in(B,relation_dom(relation_dom_restriction(C,A)))|(in(B,relation_dom(C))&in(B,A))))&(![A,B]: (in(B,relation_dom(relation_dom_restriction(C,A)))|(~in(B,relation_dom(C))|~in(B,A))))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f101])).
% 0.09/0.51 fof(f105,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(relation_dom_restriction(X0,X2)))|~in(X1,relation_dom(X0))|~in(X1,X2))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f102])).
% 0.09/0.51 fof(f154,plain,(
% 0.09/0.51 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|(B=relation_dom_restriction(C,A)<=>(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f42])).
% 0.09/0.51 fof(f155,plain,(
% 0.09/0.51 ![A,B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D)))))&(B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D)))))))))),
% 0.09/0.51 inference(NNF_transformation,[status(thm)],[f154])).
% 0.09/0.51 fof(f156,plain,(
% 0.09/0.51 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(?[D]: (in(D,relation_dom(B))&~apply(B,D)=apply(C,D))))))))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f155])).
% 0.09/0.51 fof(f157,plain,(
% 0.09/0.51 ![B]: ((~relation(B)|~function(B))|(![C]: ((~relation(C)|~function(C))|((![A]: (~B=relation_dom_restriction(C,A)|(relation_dom(B)=set_intersection2(relation_dom(C),A)&(![D]: (~in(D,relation_dom(B))|apply(B,D)=apply(C,D))))))&(![A]: (B=relation_dom_restriction(C,A)|(~relation_dom(B)=set_intersection2(relation_dom(C),A)|(in(sK11_skl(A,C,B),relation_dom(B))&~apply(B,sK11_skl(A,C,B))=apply(C,sK11_skl(A,C,B))))))))))),
% 0.09/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK11_skl]),skolemize(D,sK11_skl(A,C,B))],[f156])).
% 0.09/0.51 fof(f159,plain,(
% 0.09/0.51 ![X0,X1,X2,X3]: (~relation(X0)|~function(X0)|~relation(X1)|~function(X1)|~X0=relation_dom_restriction(X1,X2)|~in(X3,relation_dom(X0))|apply(X0,X3)=apply(X1,X3))),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f157])).
% 0.09/0.51 fof(f164,plain,(
% 0.09/0.51 (?[A,B,C]: ((relation(C)&function(C))&(in(B,A)&~apply(relation_dom_restriction(C,A),B)=apply(C,B))))),
% 0.09/0.51 inference(pre_NNF_transformation,[status(thm)],[f45])).
% 0.09/0.51 fof(f165,plain,(
% 0.09/0.51 ?[C]: ((relation(C)&function(C))&(?[A,B]: (in(B,A)&~apply(relation_dom_restriction(C,A),B)=apply(C,B))))),
% 0.09/0.51 inference(miniscoping,[status(thm)],[f164])).
% 0.09/0.51 fof(f166,plain,(
% 0.09/0.51 ((relation(sK12_skl)&function(sK12_skl))&(in(sK14_skl,sK13_skl)&~apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl)=apply(sK12_skl,sK14_skl)))),
% 0.09/0.51 inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(C,sK12_skl),skolemize(A,sK13_skl),skolemize(B,sK14_skl)],[f165])).
% 0.09/0.51 fof(f167,plain,(
% 0.09/0.51 relation(sK12_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f166])).
% 0.09/0.51 fof(f168,plain,(
% 0.09/0.51 function(sK12_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f166])).
% 0.09/0.51 fof(f169,plain,(
% 0.09/0.51 in(sK14_skl,sK13_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f166])).
% 0.09/0.51 fof(f170,plain,(
% 0.09/0.51 ~apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl)=apply(sK12_skl,sK14_skl)),
% 0.09/0.51 inference(cnf_transformation,[status(thm)],[f166])).
% 0.09/0.51 fof(f179,plain,(
% 0.09/0.51 ![X0,X1]: (~relation(X0)|~function(X0)|in(X1,relation_dom(X0))|apply(X0,X1)=empty_set)),
% 0.09/0.51 inference(destructive_equality_resolution,[status(thm)],[f65])).
% 0.09/0.51 fof(f183,plain,(
% 0.09/0.51 ![X1,X2,X3]: (~relation(relation_dom_restriction(X1,X2))|~function(relation_dom_restriction(X1,X2))|~relation(X1)|~function(X1)|~in(X3,relation_dom(relation_dom_restriction(X1,X2)))|apply(relation_dom_restriction(X1,X2),X3)=apply(X1,X3))),
% 0.09/0.51 inference(destructive_equality_resolution,[status(thm)],[f159])).
% 0.09/0.51 fof(f184,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~function(relation_dom_restriction(X0,X1))|~relation(X0)|~function(X0)|~in(X2,relation_dom(relation_dom_restriction(X0,X1)))|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2))),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f183,f70])).
% 0.09/0.51 fof(f191,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(relation_dom_restriction(X0,X2)))|~in(X1,X2)|~relation(X0)|~function(X0)|apply(X0,X1)=empty_set)),
% 0.09/0.51 inference(resolution,[status(thm)],[f105,f179])).
% 0.09/0.51 fof(f192,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|in(X1,relation_dom(relation_dom_restriction(X0,X2)))|~in(X1,X2)|apply(X0,X1)=empty_set)),
% 0.09/0.51 inference(duplicate_literals_removal,[status(thm)],[f191])).
% 0.09/0.51 fof(f199,plain,(
% 0.09/0.51 ![X0]: (~relation(X0)|~function(X0)|in(sK14_skl,relation_dom(relation_dom_restriction(X0,sK13_skl)))|apply(X0,sK14_skl)=empty_set)),
% 0.09/0.51 inference(resolution,[status(thm)],[f192,f169])).
% 0.09/0.51 fof(f219,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(relation_dom_restriction(X0,X2)))|apply(relation_dom_restriction(X0,X2),X1)=apply(X0,X1)|~relation(X0)|~function(X0))),
% 0.09/0.51 inference(resolution,[status(thm)],[f184,f90])).
% 0.09/0.51 fof(f220,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|~in(X1,relation_dom(relation_dom_restriction(X0,X2)))|apply(relation_dom_restriction(X0,X2),X1)=apply(X0,X1))),
% 0.09/0.51 inference(duplicate_literals_removal,[status(thm)],[f219])).
% 0.09/0.51 fof(f222,plain,(
% 0.09/0.51 ![X0]: (~relation(X0)|~function(X0)|apply(relation_dom_restriction(X0,sK13_skl),sK14_skl)=apply(X0,sK14_skl)|~relation(X0)|~function(X0)|apply(X0,sK14_skl)=empty_set)),
% 0.09/0.51 inference(resolution,[status(thm)],[f220,f199])).
% 0.09/0.51 fof(f223,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2)|~relation(relation_dom_restriction(X0,X1))|~function(relation_dom_restriction(X0,X1))|apply(relation_dom_restriction(X0,X1),X2)=empty_set)),
% 0.09/0.51 inference(resolution,[status(thm)],[f220,f179])).
% 0.09/0.51 fof(f225,plain,(
% 0.09/0.51 ![X0]: (~relation(X0)|~function(X0)|apply(relation_dom_restriction(X0,sK13_skl),sK14_skl)=apply(X0,sK14_skl)|apply(X0,sK14_skl)=empty_set)),
% 0.09/0.51 inference(duplicate_literals_removal,[status(thm)],[f222])).
% 0.09/0.51 fof(f226,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2)|~function(relation_dom_restriction(X0,X1))|apply(relation_dom_restriction(X0,X1),X2)=empty_set)),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f223,f70])).
% 0.09/0.51 fof(f231,plain,(
% 0.09/0.51 ~relation(sK12_skl)|apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl)=apply(sK12_skl,sK14_skl)|apply(sK12_skl,sK14_skl)=empty_set),
% 0.09/0.51 inference(resolution,[status(thm)],[f225,f168])).
% 0.09/0.51 fof(f236,plain,(
% 0.09/0.51 apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl)=apply(sK12_skl,sK14_skl)|apply(sK12_skl,sK14_skl)=empty_set),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f231,f167])).
% 0.09/0.51 fof(f237,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2)|apply(relation_dom_restriction(X0,X1),X2)=empty_set|~relation(X0)|~function(X0))),
% 0.09/0.51 inference(resolution,[status(thm)],[f226,f90])).
% 0.09/0.51 fof(f238,plain,(
% 0.09/0.51 ![X0,X1,X2]: (~relation(X0)|~function(X0)|apply(relation_dom_restriction(X0,X1),X2)=apply(X0,X2)|apply(relation_dom_restriction(X0,X1),X2)=empty_set)),
% 0.09/0.51 inference(duplicate_literals_removal,[status(thm)],[f237])).
% 0.09/0.51 fof(f243,plain,(
% 0.09/0.51 ![X0,X1]: (~relation(sK12_skl)|apply(relation_dom_restriction(sK12_skl,X0),X1)=apply(sK12_skl,X1)|apply(relation_dom_restriction(sK12_skl,X0),X1)=empty_set)),
% 0.09/0.51 inference(resolution,[status(thm)],[f238,f168])).
% 0.09/0.51 fof(f248,plain,(
% 0.09/0.51 ![X0,X1]: (apply(relation_dom_restriction(sK12_skl,X0),X1)=apply(sK12_skl,X1)|apply(relation_dom_restriction(sK12_skl,X0),X1)=empty_set)),
% 0.09/0.51 inference(forward_subsumption_resolution,[status(thm)],[f243,f167])).
% 0.09/0.51 fof(f261,plain,(
% 0.09/0.51 apply(relation_dom_restriction(sK12_skl,sK13_skl),sK14_skl)=empty_set),
% 0.09/0.52 inference(resolution,[status(thm)],[f248,f170])).
% 0.09/0.52 fof(f264,plain,(
% 0.09/0.52 ~empty_set=apply(sK12_skl,sK14_skl)),
% 0.09/0.52 inference(backward_demodulation,[status(thm)],[f261,f170])).
% 0.09/0.52 fof(f265,plain,(
% 0.09/0.52 empty_set=apply(sK12_skl,sK14_skl)|apply(sK12_skl,sK14_skl)=empty_set),
% 0.09/0.52 inference(backward_demodulation,[status(thm)],[f261,f236])).
% 0.09/0.52 fof(f266,plain,(
% 0.09/0.52 empty_set=apply(sK12_skl,sK14_skl)),
% 0.09/0.52 inference(duplicate_literals_removal,[status(thm)],[f265])).
% 0.09/0.52 fof(f267,plain,(
% 0.09/0.52 $false),
% 0.09/0.52 inference(forward_subsumption_resolution,[status(thm)],[f266,f264])).
% 0.09/0.52 % SZS output end CNFRefutation for theBenchmark.p
% 0.09/0.54 % Elapsed time: 0.166401 seconds
% 0.09/0.54 % CPU time: 1.047146 seconds
% 0.09/0.54 % Total memory used: 124.993 MB
% 0.09/0.54 % Net memory used: 123.800 MB
%------------------------------------------------------------------------------